We present improved parameterized algorithms for the Feedback Vertex Set problem on both unweighted and weighted graphs. Both algorithms run in time O(5kn). For unweighted graphs, our algorithm either constructs a feedback vertex set of size bounded by k in a given graph G, or reports that no such a feedback vertex set exists in G. For weighted graphs, our algorithm either constructs a minimum-...

In this paper we prove a discrete version of Tanaka’s Theorem [19] for the Hardy-Littlewood maximal operator in dimension n = 1, both in the non-centered and centered cases. For the non-centered maximal operator f M we prove that, given a function f : Z→ R of bounded variation, Var(f Mf) ≤ Var(f), where Var(f) represents the total variation of f . For the centered maximal operator M we prove th...

An old conjecture of Ringel states that every tree with m edges decomposes the complete graph K2m+1. The best lower bound for the order of a complete graph decomposed by a given tree with m edge is O(m). We show that asymptotically almost surely a random tree with m edges and p = 2m + 1 a prime decomposes K2m+1(r) for every r ≥ 2, the graph obtained from the complete graph K2m+1 by replacing ea...

Psychologists have been taking an increasing interest in the writing process over the last decade and models of human cognition and task behaviour during writing are emerging (see e.g., Hayes and Flower 1980, Sharples et al 1989). Though we are far short of a complete model of this process several basic components have been identified and most theorists allude to these at some stage in their de...

In this paper we present eÆcient algorithms to solve domination set problem for the class of bounded tolerance graphs. The class of bounded tolerance graphs includes interval graphs and permtation graph as subclasses. Our solution to domination set problem has improved bounds for time complexity than the algorithm for the general co-comparability graphs which can as well be used for bounded tol...

A k-bounded recognizable pattern language is the set of all k-bounded patterns that are obtained as behaviors of a pattern automaton. The emptiness and the equality problems for k-bounded behaviors of pattern automata are proved to be decidable. Moreover, we examine their relationship with context free pattern grammars, which are basically the hyperedge replacement grammars on planar directed a...